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www.the-cryosphere.net/9/781/2015/ doi:10.5194/tc-9-781-2015

© Author(s) 2015. CC Attribution 3.0 License.

Sensitivity of airborne geophysical data to sublacustrine and

near-surface permafrost thaw

B. J. Minsley1, T. P. Wellman2, M. A. Walvoord3, and A. Revil4,5

1USGS, Crustal Geophysics and Geochemistry Science Center, Denver, Colorado, USA 2USGS, Colorado Water Science Center, Denver, Colorado, USA

3USGS, National Research Program, Denver, Colorado, USA

4Colorado School of Mines, Department of Geophysics, Golden, Colorado, USA 5ISTerre, UMR CNRS 5275, Université de Savoie, Le Bourget du Lac, France Correspondence to: B. J. Minsley (bminsley@usgs.gov)

Received: 20 October 2014 – Published in The Cryosphere Discuss.: 10 December 2014 Revised: 19 March 2015 – Accepted: 5 April 2015 – Published: 27 April 2015

Abstract. A coupled hydrogeophysical forward and in-verse modeling approach is developed to illustrate the abil-ity of frequency-domain airborne electromagnetic (AEM) data to characterize subsurface physical properties associated with sublacustrine permafrost thaw during lake-talik forma-tion. Numerical modeling scenarios are evaluated that con-sider non-isothermal hydrologic responses to variable forc-ing from different lake depths and for different hydrologic gradients. A novel physical property relationship connects the dynamic distribution of electrical resistivity to ice sat-uration and temperature outputs from the SUTRA ground-water simulator with freeze–thaw physics. The influence of lithology on electrical resistivity is controlled by a surface conduction term in the physical property relationship. Re-sistivity models, which reflect changes in subsurface condi-tions, are used as inputs to simulate AEM data in order to explore the sensitivity of geophysical observations to per-mafrost thaw. Simulations of sublacustrine talik formation over a 1000-year period are modeled after conditions found in the Yukon Flats, Alaska. Synthetic AEM data are analyzed with a Bayesian Markov chain Monte Carlo algorithm that quantifies geophysical parameter uncertainty and resolution. Major lithological and permafrost features are well resolved by AEM data in the examples considered. The subtle geome-try of partial ice saturation beneath lakes during talik forma-tion cannot be resolved using AEM data, but the gross char-acteristics of sub-lake resistivity models reflect bulk changes in ice content and can identify the presence of a talik. A final synthetic example compares AEM and ground-based

electro-magnetic responses for their ability to resolve shallow per-mafrost and thaw features in the upper 1–2 m below ground outside the lake margin.

1 Introduction

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damage buildings, roadways, or pipelines due to ground set-tling, and thermal erosion that can alter coastlines and land-scape stability (Larsen et al., 2008; Nelson et al., 2002).

Several investigations have shown the significance of cli-mate and advective heat transport in controlling the distribu-tion of permafrost in hydrologic systems (Bense et al., 2009; Rowland et al., 2011; Wellman et al., 2013). These results yield important insight into the mechanistic behavior of cou-pled thermal–hydrologic systems and are a means for pre-dicting the impact on permafrost from a wide range of cli-mate and hydrologic conditions. However, few techniques are capable of assessing the distribution of permafrost, and most approaches only capture a single snapshot in time.

Satellite remote-sensing techniques have proven useful in detecting the distribution and changes in shallow permafrost, vegetation, and active layer thickness over large areas (Liu et al., 2012; Panda et al., 2010; Pastick et al., 2014) but are only sensitive to very near-surface properties. Borehole cores and downhole temperature or geophysical logs provide direct in-formation about permafrost and geologic structures but tend to be sparsely located and are not always feasible in remote areas. Geophysical methods are necessary for investigating subsurface physical properties over large and/or remote ar-eas. Recent examples of geophysical surveys aimed at char-acterizing permafrost in Alaska include an airborne electro-magnetic (AEM) survey used to delineate geologic and per-mafrost distributions in an area of discontinuous perper-mafrost (Minsley et al., 2012), ground-based electrical measurements used to assess shallow permafrost aggradation near recently receded lakes (Briggs et al., 2014), electrical and electro-magnetic surveys used to characterize shallow active layer thickness and subsurface salinity (Hubbard et al., 2013), and surface nuclear magnetic resonance soundings used to infer the thickness of unfrozen sediments beneath lakes (Parsekian et al., 2013). A challenge with geophysical methods, how-ever, is that geophysical properties (e.g., electrical resistiv-ity) are only indirectly sensitive to physical properties of in-terest (e.g., lithology, water content, thermal state). In addi-tion, various physical properties can produce similar electri-cal resistivity values. Therefore, it is critielectri-cally important to understand the relationship between geophysical properties and the ultimate physical properties and processes of interest (Minsley et al., 2011; Rinaldi et al., 2011).

The non-isothermal hydrologic simulations of Wellman et al. (2013) predict the evolution of lake taliks (unfrozen sub-lacustrine areas in permafrost regions) in a two-dimensional axis-symmetric model under different environmental scenar-ios (e.g., lake size, climate, groundwater flow regime). Here, we investigate the ability of geophysical measurements to re-cover information about the underlying spatial distribution of permafrost and hydrologic properties. This is accomplished in three steps: (1) development of a physical property relation that connects permafrost and hydrologic properties to geo-physical properties, (2) generation of synthetic geogeo-physical data that would be expected for various permafrost

hydro-logic conditions that occur during simulated lake-talik for-mation, and (3) inversion of the synthetic geophysical data using realistic levels of noise to investigate the ability to re-solve specific physical features of interest. Our focus is on electromagnetic geophysical methods as these types of data have previously been acquired near Twelvemile Lake in the Yukon Flats, Alaska (Ball et al., 2011; Minsley et al., 2012); this lake is also the basis for the lake simulations discussed by Wellman et al. (2013).

2 Methods

2.1 Coupled thermal–hydrologic simulations

Wellman et al. (2013) describe numerical simulations of lake-talik formation in watersheds modeled after those found in the lake-rich Yukon Flats of interior Alaska. Modeling experiments used the SUTRA groundwater modeling code (Voss and Provost, 2002) enhanced with capabilities to simu-late freeze–thaw processes (McKenzie and Voss, 2013). The phase change between ice and liquid water occurs over a specified temperature range and accounts for latent heat of fusion as well as changes in thermal conductivity and heat capacity for ice–water mixtures. Ice content also changes the effective permeability, thereby altering subsurface flow-paths and enforcing a strong coupling between hydraulic and thermal processes. The modeling domain, which is adapted for this study, is axis-symmetric with a central lake and upwards-sloping ground surface that rises from an elevation of 500 m atr=0 to 520 m at the outer extent of the model,

r=1800 m (Fig. 1). The model uses a layered geology con-sistent with the Yukon Flats (Minsley et al., 2012; Williams, 1962), with defined hydrologic and geophysical parameters for each layer summarized in Table 1. Initial permafrost con-ditions prior to lake formation were established by running the model to steady state under hydrostatic conditions with a constant temperature of−2.25◦C applied to the land sur-face, which produces a laterally continuous permafrost layer extending to a depth of about 90 m.

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lake depth = 3 m, 6 m, 9 m, 12 m

Unit 2 Gravelly sand

Unit 3 Lacustrine silt Unit 1

Silty sand

Distance (m)

Elevation (m)

420 430 440 450 460 470 480 490 500 510 520

0 200 400 600 800 1000 1200 1400 1600 1800

Figure 1. Axis-symmetric model geometry indicating different lithologic units and simulated lake depths/extents.

2.2 A physical property relationship

Electrical resistivity is the primary geophysical property of interest for the electromagnetic geophysical methods used in this study. It is well established that resistivity is sensitive to basic physical properties such as unfrozen water content, soil or rock texture, and salinity (Palacky, 1987). Here, we build on earlier efforts to simulate the electrical properties of ice-saturated media (Hauck et al., 2011) by using a modified form of Archie’s Law (Archie, 1942) that also incorporates surface conduction effects (Revil, 2012) to predict the dy-namic electrical resistivity structure for the evolving state of temperature and ice saturation (Si) in the talik simulations. Bulk electrical conductivity is described by Revil (2012) as

σ =S

n w

F

σf+m Sw−nF−1

σs

, (1)

where σ is the bulk electrical conductivity [S m−1]; S w is the fractional water saturation [–] in the pore space, where

Sw=1−Si;σfis the conductivity of the saturating pore fluid [S m−1];mis the Archie cementation exponent [–];nis the Archie saturation exponent [–];F is the formation factor [–], whereF =φ−mandφis the matrix porosity [–]; andσs is the conductivity [S m−1] associated with grain surfaces. The Archie exponentsmandnare known to vary as a function of pore geometry; here, we usem=n=1.5, which is appropri-ate for unconsolidappropri-ated sediments (Sen et al., 1981). Simula-tion results are presented as electrical resistivity [m], which is the inverse of the conductivity, i.e.,ρ=1/σ.

The first term in Eq. (1) describes electrical conduction within the pore fluid, where fluid conductivity is defined as

σf=Fc X

i

βi|zi|Ci. (2)

The summation in Eq. (2) is over all dissolved ionic species (Na+ and Cl− are assumed to be the primary constituents in this study), whereFcis Faraday’s constant [C mol−1] and

Ci,βi, andziare the concentration [mol L−1], ionic mobility [m2V−1s−1], and valence of theith species, respectively.

Table 1. Description of geologic units and physical properties used in numerical simulations. Entries separated by commas represent parameters with different values for each of the lithologic units.

Geologic unit properties

Lithology:

Unit 1 Sediment (silty sand)

Unit 2 Sediment (gravelly sand)

Unit 3 Lacustrine silt

Unit depth range [m] 0–2, 2–30, 30–250

Porosity [–] 0.25, 0.25, 0.20

Geophysical parameters

Archie cementation exponent (m) [–] 1.5 Archie saturation exponent (n) [–] 1.5 Water salinity (C) [ppm] 250 (Si=0)

Na+ionic mobility (β) [m2V−1s−1] 5.8×10−8(25◦C) Cl−ionic mobility (β) [m2V−1s−1] 7.9×10−8(25◦C) Na+surface ionic mobility (βs) [m2V−1s−1] 0.51×10−8(25◦C)

Grain mass density (ρg) [kg m−3] 2650

Cation exchange capacity (χ) [C kg−1] 200, 10, 500 Salinity exponent (a) [–] 0.8

Surface conduction effects, described by the second term in Eq. (1), are related to the chemistry at the pore–water inter-face, and can be important in fresh water (low conductivity) systems at low porosity (high ice saturation). Additionally, the surface conduction term provides a means for describing the conductivity behavior for different lithologies, as will be described below. The surface conductivity is given by

σs= 2 3

φ

1−φ

βsQv, (3)

whereβsis the cation mobility [m2V−1s−1] for counterions in the electrical double layer at the grain-water interface (Re-vil et al., 1998) andQvis the excess electrical charge density [C m−3] in the pore volume, and

Qv=Sw−1ρg 1φ

φ

χ , (4)

whereρgis the mass density of the grains [kg m−3] andχis the cation exchange capacity [C kg−1]. Changes inχ, repre-sentative of bulk differences in clay mineral content, are used to differentiate the electrical signatures of the lithologic units in this study (Table 1).

The temperature,T [C], dependence of ionic mobility af-fects both the fluid conductivity (Eq. 2) and surface conduc-tivity (Eq. 3), where mobility is approximated as a linear function of temperature (Keller and Frischknecht, 1966; Sen and Goode, 1992) as

β (T )=βT=25◦C[1+0.019(T−25)]. (5)

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1995), leading to a corresponding increase in fluid conduc-tivity according to Eq. (2). To describe this dependence of salinity on ice saturation,C(Si), we use the expression

C (Si)=CSi=0S −α

w , (6)

whereα∼0.8 accounts for loss of solute from the pore space due to diffusion or other transport processes andSi=1−Sw. Information about the different lithologic units described by Wellman et al. (2013) that are also summarized in Table 1 are used to define static model properties such as porosity, grain mass density, cation exchange capacity, and Archie’s exponents. Dynamic outputs from the SUTRA simulations, including temperature and ice saturation, are combined with the static variables in Eqs. (1)–(6) to predict the evolving electrical resistivity structure.

2.3 Geophysical forward simulations

Synthetic AEM data are simulated for each snapshot of pre-dicted bulk resistivity values using nominal system parame-ters based on the Fugro RESOLVE1frequency-domain AEM system that was used in the Yukon Flats survey (Minsley et al., 2012). The RESOLVE system consists of five horizon-tal coplanar (HCP) transmitter–receiver coil pairs separated by approximately 7.9 m that operate at frequencies 0.378, 1.843, 8.180, 40.650, and 128.510 kHz and one vertical coax-ial coil pair with 9 m separation that operates at 3.260 kHz. Oscillating currents and associated magnetic fields created by the transmitter coils induce electrical currents in the sub-surface that, in turn, generate secondary magnetic fields that are recorded by the receiver coils (Siemon, 2006; Ward and Hohmann, 1988). Data are reported as in-phase and quadra-ture components of the secondary field in parts per million (ppm) of the primary field, and responses as a function of fre-quency can be converted through mathematical inversion to estimates of electrical resistivity as a function of depth (e.g., Farquharson et al., 2003). Data are simulated at the nomi-nal survey elevation of 30 m above ground surface using the one-dimensional modeling algorithm described in Minsley (2011), which follows the standard electromagnetic theory presented by Ward and Hohmann (1988).

The vertical profile of resistivity as a function of depth is extracted at each survey location and is used to simulate for-ward geophysical responses. There are 181 sounding loca-tions for each axis-symmetric model, starting at the center of the lake (r=0 m) and moving to the edge of the model do-main (r=1800 m) in 10 m increments. Each vertical resis-tivity profile extends to 200 m depth, which is well beyond the depth to which we expect to recover parameters in the geophysical inversion step. A center-weighted five-point fil-ter with weights equal to [0.0625, 0.25, 0.375, 0.25, 0.0625] is used to average neighboring bulk resistivity values at each 1Any use of trade, product, or firm names is for descriptive

pur-poses only and does not imply endorsement by the US Government.

depth before modeling in order to partly account for the lat-eral sensitivity of AEM systems (Beamish, 2003). Forward simulations are repeated for each of the 50 simulation times between output of 0 and 1000 years from SUTRA, resulting in 9050 data locations per modeling scenario.

Synthetic ground-based electromagnetic data presented in Sect. 3.3 are simulated using nominal system parameters based on the GEM-2 instrument (Huang and Won, 2003). The GEM-2 has a single HCP transmitter–receiver pair sepa-rated by 1.66 m, and data are simulated at six frequencies: 1.5, 3.5, 8.1, 19, 43, and 100 kHz. A system elevation of 1 m above ground is assumed, which is typical for this hand-carried instrument.

2.4 Parameter estimation and uncertainty quantification

The inverse problem involves estimating subsurface resistiv-ity values given the simulated forward responses and realistic assumptions about data errors. Geophysical inversion is in-herently uncertain; there are many plausible resistivity mod-els that are consistent with the measured data. In addition, the ability to resolve true resistivity values is limited both by the physics of the AEM method and the level of noise in the data. Here, we use a Bayesian Markov chain Monte Carlo (McMC) algorithm developed for frequency-domain electromagnetic data (Minsley, 2011) to explore the ability of simulated AEM data to recover the true distribution of subsurface resistivity values at 20-year intervals within the 1000-year lake-talik simulations. This McMC approach is an alternative to traditional inversion methods that find a single “optimal” model that minimizes a combined measure of data fit and model regularization (Aster et al., 2005). Although computationally more demanding, McMC methods allow for comprehensive model appraisal and uncertainty quantifica-tion. AEM-derived resistivity estimates for the simulations considered here will help guide interpretations of future field data sets, identifying the characteristics of relatively young versus established thaw under different hydrologic condi-tions.

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due to assumptions about model parameterization. Instead, trans-dimensional sampling rules (Green, 1995; Sambridge et al., 2013) are used to allow the number of unknown layers to be one of the unknowns. That is, the unknown parameters for each model include the number of layers, layer interface depths, and resistivity values for each layer.

Numerous measures and statistics are generated from the ensemble of plausible resistivity models, such as the single most-probable model, the probability distribution of resistiv-ity values at any depth, the probabilresistiv-ity distribution of where layer interfaces occur as a function of depth, and the proba-bility distribution of the number of layers (model complex-ity) needed to fit the measured data. A detailed description of the McMC algorithm can be found in Minsley (2011). Finally, probability distributions of resistivity are combined with assumptions about the distribution of resistivity values for any lithology and/or ice content in order to make a prob-abilistic assessment of lithology or ice content, as illustrated below.

3 Results

3.1 Electrical resistivity model development

Information about the different lithologic units described by Wellman et al. (2013) that are also summarized in Table 1 are used to define static model properties such as porosity, grain mass density, cation exchange capacity, and Archie’s exponents. Dynamic outputs from the SUTRA simulations, including temperature and ice saturation, are combined with the static variables in Eqs. (1)–(6) to predict the evolving electrical resistivity structure. The behavior of bulk resistiv-ity as a function of ice saturation is shown in Fig. 2. Separate curves are shown for a range ofχ(cation exchange capacity) values, which are the primary control in defining offset resis-tivity curves for different lithologies, where increasingχ is generally associated with more fine-grained material such as silt or clay.

For each of the 1000-year simulations, the static variables summarized in Table 1 are combined with the spatially and temporally variable state variablesT andSi output by SU-TRA to predict the distribution of bulk resistivity at each time step using Eqs. (1)–(6). An example of SUTRA output vari-ables for the 6 m deep gaining lake scenario at 240 years (the approximate sub-lake talik breakthrough time for that sce-nario) is shown in Fig. 3a and b, and the predicted resistivity for this simulation step is shown in Fig. 3c. The influence of different lithologic units is clearly manifested in the pre-dicted resistivity values, whereas lithology is not overly ev-ident in the SUTRA state variables. For a single unit, there is a clear difference in resistivity for frozen versus unfrozen conditions. Across different units, there is a contrast in re-sistivity when both units are frozen or unfrozen. Rere-sistivity can therefore be a valuable indicator of both geologic and ice

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

101

102

103

104

Ice saturation

Resistivity (ohm−m)

Unit 1, χ= 200

Unit 2, χ = 10

Unit 3, χ = 500

Unit 4, χ = 1000

Figure 2. Bulk resistivity as a function of ice saturation using the physical properties defined for each of the lithologic units described in Table 1.

content variability. However, there is also ambiguity in resis-tivity values as both unfrozen unit 2 and frozen unit 3 appear to have intermediate resistivity values of approximately 100– 300m (Fig. 3c) and cannot be characterized by their resis-tivity values alone. This ambiguity in resisresis-tivity can only be overcome by additional information such as borehole data or prior knowledge of geologic structure. Synthetic bulk resis-tivity values according to Eq. (1) are shown in Fig. 4 for the four different lake depths (3, 6, 9, and 12 m) at three different simulation times (100, 240, and 1000 years) output from the hydrostatic/current climate condition simulations.

Lithology and ice saturation are the primary factors that control simulated resistivity values (Fig. 2), though ice sat-uration is a function of temperature. The empirical relation between temperature and bulk resistivity is shown in Fig. 3d by cross-plotting values from Fig. 3b and c. Within each lithology resistivity is relatively constant above 0◦C, with a rapid increase in resistivity for temperatures below 0◦C. This result is very similar to the temperature–resistivity rela-tionships illustrated by Hoekstra et al. (1975, Fig. 1), lend-ing confidence to our physical property definitions described earlier. Above 0◦C, the slight decrease in resistivity is due to the temperature dependency of fluid resistivity. The rapid increase in resistivity below 0◦C is primarily caused by re-ductions in effective porosity due to increasing ice satura-tion, though changes in surface conductivity and salinity at increasing ice saturation are also contributing factors. Below

−1◦C, the change in resistivity values as a function of

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S i

Resistivity (ohm-m)

Distance (m)

Distance (m)

Elevation (m)

Elevation (m)

A

C

Temperature (C)

Distance (m)

Elevation (m)

B

D

Unit 1

Unit 3 Unit 2

Temperature (C)

Resistivity (ohm-m)

300-1500 500

450

400

350 550

-1000 -500 0 500 1000 1500 300-1500 500

450

400

350 550

-1000 -500 0 500 1000 1500

300-1500 500

450

400

350 550

-1000 -500 0 500 1000 1500 101 -6 -4 -2 0 2 4 102

103

104

0

-5 5

0 0.5 1

25 5,000

1,000

300

100

Figure 3. SUTRA model outputs and geophysical transformations from the 6 m gaining lake simulation at 240 years. Ice saturation (a) and temperature (b) are converted to predictions of bulk resistivity (c). Variability in resistivity as a function of temperature is indicated in (d) for lithologic units 1–3.

Distance (m) Distance (m) Distance (m)

Elevation (m)

Elevation (m)

Elevation (m)

Elevation (m)

3 m Lake depth

6 m Lake depth

9 m Lake depth

12 m Lake depth

300 -1000 500 450 400 350

0 1000 100 years

300 -1000 500 450 400 350

0 1000 240 years

300 -1000 500 450 400 350

0 1000 1,000 years

300 -1000 500 450 400

350

0 1000 300 -1000

500 450 400 350

0 1000 300 -1000

500 450 400

350

0 1000

300 -1000 500

450 400 350

0 1000 300 -1000

500 450 400

350

0 1000 300 -1000

500 450 400

350

0 1000

300 -1000 500 450 400 350

0 1000 300 -1000

500 450 400 350

0 1000 300 -1000

500 450 400

350

0 1000 25 5,000

1,000

300

100 Resistivity (ohm-m)

A B C

D E F

G H I

J K L

Figure 4. Synthetic bulk resistivity images under hydrostatic flow and current climate conditions. Lake depths of 3 m (a–c), 6 m (d–f), 9 m (g–i), and 12 m (j–l) are illustrated at simulation times 100, 240, and 1000 years.

their ability to discern differences among very high resistivity values, as discussed later, this artifact does not significantly impact the results presented here.

3.2 Parameter estimation and uncertainty quantification

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re-Figure 5. Mean resistivity model extracted from McMC ensembles. Results are shown for the 6 m deep hydrostatic lake scenario outputs at (a) 100 years, (b) 240 years, and (c) 1000 years.

cover estimates of the original resistivity values according to the approach outlined in Sect. 2.4, assuming 4 % data error with an absolute error floor of 5 ppm. Resistivity parameter estimation results for the 6 m deep hydrostatic lake scenario (Fig. 4d–f) are shown in Fig. 5. At each location along the profile, the average resistivity model as a function of depth is calculated from the McMC ensemble of 100 000 plausible models. The overall pattern of different lithologic units and frozen/unfrozen regions is accurately depicted in Fig. 5, with two exceptions that will be discussed in greater detail: (1) the specific distribution of partial ice saturation beneath the lake before thaw has equilibrated (Fig. 5a and b) and (2) the shal-low sand layer (unit 1) that is generally too thin to be resolved using AEM data.

A point-by-point comparison of true (Fig. 4f) versus pre-dicted (Fig. 5c) resistivity values for the hydrostatic 6 m deep lake scenario at the simulation time 1000 years is shown in Fig. 6a. The cross-plot of true versus estimated resistivity values generally fall along the 1:1 line, providing a more quantitative indication of the ability to estimate the subsur-face resistivity structure. Estimates of the true resistivity val-ues for each lithology and freeze–thaw state (Fig. 6b) tend to be indistinct, appearing as a vertical range of possible values in Fig. 6a due to the inherent resolution limitations of inverse methods and parameter tradeoffs (Day-Lewis et al., 2005; Oldenborger and Routh, 2009). Although the greatest point density for both frozen and unfrozen silts (unit 3) falls along the 1:1 line, resistivity values for these components of the model are also often overestimated; this is likely due to un-certainties in the location of the interface between the silt and

gravel units. This is in contrast with the systematic underes-timation of frozen gravel resistivity values due to the inabil-ity to discriminate very high resistivinabil-ity values using electro-magnetic methods (Ward and Hohmann, 1988). Frozen sands (true log resistivity∼2.8 in Fig. 6b) are also systematically overestimated in Fig. 6a; in this case, due to the inability to resolve this relatively thin resistive layer.

While useful, single “best” estimates of resistivity values at any location (Fig. 6) are not fully representative of the in-formation contained in the AEM data and associated model uncertainty. From the McMC analysis of 100 000 models at each data location, estimates of the posterior probability den-sity function (pdf) of resistivity are generated for each point in the model. Probability distributions are extracted from a depth of 15 m, within the gravel layer (unit 2), at one location where unfrozen conditions exist (r=0 m) and a second loca-tion outside the lake extent (r=750 m) where the ground re-mains frozen (Fig. 7a). Results from a depth of 50 m, within the silt layer (unit 3), are shown in Fig. 7b. With the excep-tion of the frozen gravels, the resistivity of which tends to be underestimated, the peak of each pdf is a good estimate of the true resistivity value at that location.

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1 1.5 2 2.5 3 3.5 4 0

0.01 0.02 0.03

frequency

1 1.5 2 2.5 3 3.5 4

1 1.5 2 2.5 3 3.5 4

Estimated resistivity (log

10

ohm−m)

True resistivity (log10 ohm−m)

A

B

frozen gravel

frozen sand frozen

silt

unfrozen gravel lake

unfrozen silt unfrozen

sand & transitional silt lake

unfrozen silt unfrozen sand & transitional silt

unfrozen gravel

frozen silt

frozen sand

frozen gravel

True resistivity (log10 ohm−m)

Figure 6. Performance of geophysical parameter estimation in re-covering true parameter values. (a) True versus McMC-estimated resistivity values for the hydrostatic 6 m deep lake scenario at simu-lation time 1000 years compared with the frequency distribution of true resistivity values (b). Estimated resistivity values generally fall along the dashed 1:1 line in (a), with the exception of underpredic-tion of the resistive frozen gravels, overpredicunderpredic-tion of the thin surfi-cial frozen sand, and some overprediction of the frozen silt where it is in contact with frozen gravel.

less than 0.5. Probability estimates of ice content less than 50 % and greater than 95 % for the four distributions shown in Fig. 7 are summarized in Table 2. High probabilities of ice content exceeding 95 % are associated with the r=750 m location outside the lake extent, whereas high probability of ice content below the 50 % threshold are observed atr=0 beneath the center of the lake. The pdfs for each lithology shown in Fig. 7 are end-member examples of frozen and un-frozen conditions. Within a given lithology, a smooth tran-sition from the frozen-state pdf to the unfrozen-state pdf is observed as thaw occurs, with corresponding transitions in the calculated ice threshold probabilities.

A

B

101 102 103 104

0 0.02 0.04 0.06 0.08 0.1 0.12

Estimated resistivity (ohm−m)

Probability

101

102

103

104 0

0.02 0.04 0.06 0.08 0.1

Estimated resistivity (ohm−m)

Probability

0.0 0.5 0.75 0.9 0.95 0.99

0.0 0.5 0.75 0.9 0.95 0.99 Ice Saturation

Ice Saturation

true value frozen (x = 750 m) unfrozen (x = 0 m)

Unit #2 depth = 15 m

Unit #3 depth = 50 m

true value frozen (x = 750 m) unfrozen (x = 0 m)

Figure 7. McMC-estimated resistivity posterior distributions within frozen and unfrozen unit 2 gravels (a) and frozen and unfrozen unit 3 silts (b) for the hydrostatic 6 m deep lake scenario at 1000 years. Unfrozen resistivity distributions are extracted beneath the center of the lake (r=0) at depths of 15 and 50 m for the gravels and silts, respectively. Frozen distributions are extracted at the same depths but atr=750 m. The upperx-axis labels indicate approximate ice saturation based on the lithology-dependent ice saturation versus resistivity curves shown in Fig. 2.

Table 2. Probability of ice saturation falling above or below spec-ified thresholds based on the McMC-derived resistivity probability distributions shown in Fig. 7.

p(ice<0.5) p(ice>0.95)

Unit 2 (gravel),r=0 m 0.76 0.05

Unit 2 (gravel),r=750 m 0.00 0.88

Unit 3 (silt),r=0 m 0.76 0.05

Unit 3 (silt),r=750 m 0.00 0.98

Further illustration of the spatial and temporal changes in resistivity pdfs are shown in Fig. 8. The resistivity pdf is dis-played as a function of distance from the lake center at the same depths (15 and 50 m) shown in Fig. 7, corresponding to gravel (Fig. 8a, c, and e) and silt (Fig. 8b, d, and f) locations. High probabilities, i.e., the peaks in Fig. 7, correspond to dark-shaded areas in Fig. 8. Images are shown for three dif-ferent time steps in the SUTRA simulation for the hydrostatic 6 m deep lake scenario: 100 years (Fig. 8a and b), 240 years (Fig. 8c and d), and 1000 years (Fig. 8e and f). Approxi-mate ice-saturation values, translated from the ice versus re-sistivity relationships for each lithology shown in Fig. 2, are displayed on the right axis of each panel in Fig. 8, and true resistivity values are plotted as a dashed line. Observations from Fig. 8 include the following:

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A

F E

D C

B

p(resistivity) True value

0 200 400 600 800 10001200 140016001800

Distance (m) 100 years, 15 m depth

Resistivity (ohm-m) 0 Ice Saturation

0.5 0.75 0.9 0.95 0.99

102 103 104

0 200 400 600 800 10001200 140016001800

Distance (m) 240 years, 15 m depth

Resistivity (ohm-m) 0 Ice Saturation

0.5 0.75 0.9 0.95 0.99

102 103 104

0 200 400 600 800 10001200140016001800

1,000 years, 15 m depth

Resistivity (ohm-m) 0 Ice Saturation

0.5 0.75 0.9 0.95 0.99

102 103 104

Distance (m)

0 200 400 600 800 10001200140016001800

Distance (m) 100 years, 50 m depth

Resistivity (ohm-m) 0 Ice Saturation

0.5 0.75 0.9 0.95 0.99

102 103

101

0 200 400 600 800 10001200140016001800

Distance (m) 240 years, 50 m depth

Resistivity (ohm-m) 0 Ice Saturation

0.5 0.75 0.9 0.95 0.99

102 103

101

0 200 400 600 800 10001200140016001800

1,000 years, 50 m depth

Resistivity (ohm-m) 0 Ice Saturation

0.5 0.75 0.9 0.95 0.99

102 103

101

Distance (m)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Lake edge

Figure 8. Resistivity probability distributions for the hydrostatic 6 m deep lake scenario at simulation times 100 years (a–b), 240 years (c–d), and 1000 years (e–f). Shading in each image represents the probability distribution at depths of 15 m (a, c, e) and 50 m (b, d, f) from the lake center (r=0 m) to the edge of the model (r=1800 m). Dashed lines indicate the true resistivity values. Ice saturation is displayed on the right axis of each image and is defined empirically for each lithology using the relationships in Fig. 2.

the silt unit, suggesting better resolution of shallower resistivity values within the gravel layer. It should be noted, however, that this improved resolution does not imply improved model accuracy; in fact, the highest probability region slightly underestimates the true re-sistivity value.

2. Probability distributions for the silt layer track the true values but with greater uncertainty.

3. Inside the lake boundary, gravel resistivity values are not as well resolved compared with locations outside the lake boundary due to the loss of signal associated with the relatively conductive lake water.

4. Increasing trends in resistivity/ice saturation towards the outer extents of the lake are captured in the pdfs but are subtle.

5. Within the silt layer at early times before the talik is fully through-going (Fig. 8b and d), the AEM data are insensitive to which layer is present, hence the bi-modal resistivity distribution with peaks associated with char-acteristic silt and gravel values. This ambiguity disap-pears at later times when the low-resistivity unfrozen silt layer extends to the base of the unfrozen gravels, which is a more resolvable target (Fig. 8f).

A more detailed analysis of the changes in resistivity and ice saturation as a function of time, and for the differences between hydrostatic and gaining lake conditions, is presented in Fig. 9. Average values of resistivity/ice saturation within 100 m of the lake center are shown within the gravel layer at a depth of 15 m (Fig. 9a) and a depth of 50 m within the silt layer (Fig. 9b) at 20-year time intervals. Outputs are displayed for both 6 m deep hydrostatic and gaining lake scenarios. Thawing due to conduction occurs over the first

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0 100 200 300 400 500 600 700 800 900 1000 0

0.2 0.4 0.6 0.8 1

Time (year)

Ice Saturation

0 100 200 300 400 500 600 700 800 900 1000 0

0.2 0.4 0.6 0.8 1

Time (year)

Ice Saturation

175 250 500 1500

Resistivity (ohm−m)

30 50 150

Resistivity (ohm−m)

Unit #2 (gravel) at 15 m depth

Unit #3 (silt) at 50 m depth

Hydrostatic Gaining time of talik formation

gaining hydrostatic

Hydrostatic Gaining

A

B

Figure 9. Change in ice saturation and resistivity as a function of time. Results are shown for the 6 m deep lake hydrostatic and gain-ing lake scenarios within (a) the gravel layer, unit #2, at a depth of 15 m and (b) the silt layer, unit 3, at a depth of 50 m.

lake. This rapid loss in ice content begins after the gravel layer thaws and reaches a minimum near the 258-year time of talik formation for this scenario. These trends, captured by the AEM-derived resistivity models, are consistent with the plots of change in ice volume output from the SUTRA simulations reported by Wellman et al. (2013, Fig. 3). 3.3 Near-surface resolution

Finally, we focus on the upper sand layer (unit 1), which is generally too thin (2 m) and resistive (>600m) to be resolved using AEM data, though may be imaged using other ground-based electrical or electromagnetic geophys-ical methods. Seasonal thaw and surface runoff cause lo-cally reduced resistivity values in the upper 1 m, which is still too shallow to resolve adequately using AEM data. In practice, shallow thaw and sporadic permafrost trends are ob-served to greater depths in many locations, including inactive or abandoned channels (Jepsen et al., 2013b). To simulate these types of features, the shallow resistivity structure of the 6 m deep hydrostatic lake scenario at 1000 years is manually modified to include three synthetic “channels”. These chan-nels are not intended to represent realistic pathways relative to the lake and the hydrologic simulations; they are solely for the purpose of illustrating the ability to resolve shallow resistivity features.

Figure 10a shows the three channels in a zoomed-in view of the uppermost portion of the model outside the lake extent. Each channel is 100 m wide but with different depths: 1 m

Figure 10. Comparison of airborne and ground-based measuments for recovering shallow thaw features. (a) True shallow re-sistivity structure extracted from the hydrostatic 6 m deep lake sce-nario at a simulation time of 1000 years, shown outside of the lake extent (distance>500 m). Three shallow low-resistivity channels with thicknesses of 1, 2, and 3 m were added to the resistivity model to provide added contrast. McMC-derived results using simulated AEM data (b) and ground-based electromagnetic data (c) illustrate the capability of these systems to image shallow features.

(half the unit 1 thickness), 2 m (full unit 1 thickness), and 3 m (extending into the top of unit 2). Analysis of AEM data sim-ulated for this model, presented as the McMC average model, is shown in Fig. 10b. All three channels are clearly identified, but their thicknesses and resistivity values are overestimated and cannot be distinguished from one another. To explore the possibility of better resolving these shallow features, syn-thetic electromagnetic data are simulated using the charac-teristics of a ground-based multi-frequency electromagnetic tool (the GEM-2 instrument) that can be hand carried or towed behind a vehicle and is commonly used for shallow investigations. The McMC average model result for the sim-ulated shallow electromagnetic data is shown in Fig. 10c. An error model with 4 % relative data errors and an absolute er-ror floor of 75 ppm was used for the GEM-2 data. Channel thicknesses and resistivity values are better resolved com-pared with the AEM result, though the 1 m deep channel near

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4 Discussion

Understanding the hydrogeophysical responses to permafrost dynamics under different hydrologic and climatic conditions, and in different geological settings, is important for guid-ing the interpretation of existguid-ing geophysical data sets and also for planning future surveys. Geophysical models are inherently uncertain and ambiguous because of (1) the res-olution limitations of any geophysical method and (2) the weak or non-unique relationship between hydrologic proper-ties and geophysical properproper-ties. We have presented a general framework for coupling airborne and ground-based electro-magnetic predictions to hydrologic simulations of permafrost evolution, including a novel physical property relationship that accounts for the electrical response to changes in lithol-ogy, temperature, and ice content, as well as a rigorous anal-ysis of geophysical parameter uncertainty. Although the fo-cus here is on AEM data, other types of electrical or elec-tromagnetic measurements could be readily simulated using the same resistivity model. Future efforts will focus on the simulation of other types of geophysical data (e.g., nuclear magnetic resonance or ground penetrating radar) using the same basic modeling approach.

In the specific examples of lake-talik evolution presented here, which are modeled after the physical setting of the Yukon Flats, Alaska (Minsley et al., 2012), AEM data are shown to be generally capable of resolving large-scale per-mafrost and geological features (Fig. 5), as well as thermally and hydrologically induced changes in permafrost (Figs. 8 and 9). The Bayesian McMC analysis provides useful de-tails about model resolution and uncertainty that cannot be assessed using traditional inversion methods that produce a single “best” model. A fortuitous aspect of the Yukon Flats model is the fact that the silt layer (unit 3) is relatively con-ductive compared with the overlying gravels (unit 2), making it a good target for electromagnetic methods. If the order of these layers were reversed, if the base of permafrost were hosted in a relatively resistive lithology, or if the base of per-mafrost was significantly deeper, AEM data would not likely resolve the overall structure with such good fidelity. In addi-tion, knowledge of the stratigraphy helps to remove the ambi-guity between unfrozen gravels and frozen silts, which have similar intermediate resistivity values (Figs. 4 and 5). The methods developed here that use a physical property model to link hydrologic and geophysical properties provide the nec-essary framework to test other more challenging hydrogeo-logical scenarios.

Two key challenges for the lake-talik scenarios were iden-tified: (1) resolving the details of partial ice saturation be-neath the lake during talik formation and (2) resolving near-surface details associated with shallow thaw. The first chal-lenge is confirmed by Figs. 5 and 8, which show that AEM data cannot resolve the details of partial ice saturation be-neath a forming talik. However, there is clearly a change in the overall characteristics of the sub-lake resistivity

struc-ture as thaw increases (Fig. 9). One notable feastruc-ture is the steadily decreasing depth to the top of the low-resistivity unfrozen silt (red) beneath the lake (Fig. 5a–b) as thaw in-creases, ultimately terminating at the depth of the gravel– silt interface when fully unfrozen conditions exist (Fig. 5c). Measurements of the difference in elevation between the in-terpreted top of unfrozen silt and the base of nearby frozen gravels were used by Jepsen et al. (2013a) to classify whether or not fully thawed conditions existed beneath lakes in the Yukon Flats AEM survey described by Minsley et al. (2012). The simulations presented here support use of this metric to distinguish full versus partial thaw beneath lakes. However, without the presence of a lithological boundary, the shal-lowing base of permafrost associated with talik development beneath lakes would be much more difficult to distinguish. Finally, it is important to note that resistivity is sensitive primarily to unfrozen water content and that significant un-frozen water can remain in relatively warm permafrost that is near 0◦C, particularly in fine-grained sediments. Resistivity-derived estimates of talik boundaries defined by water con-tent may therefore differ from the thermal boundary defined at 0◦C.

The second challenge, to resolve near-surface details as-sociated with supra-permafrost thaw, is addressed in Fig. 10. For the scenarios considered here, AEM data can identify shallow thaw features but have difficulty in discriminating their specific details. There are many combinations of resis-tivity and thickness that produce the same electromagnetic response; therefore, without additional information it is not possible to uniquely characterize both thaw depth and re-sistivity. Ground-based electromagnetic data show improved sensitivity to the shallow channels and also limited sensi-tivity to the interface between resistive frozen gravels and frozen silty sands (Fig. 5). By restricting the possible values of resistivity and/or thickness for one or more layers based on prior assumptions, Dafflon et al. (2013) showed that im-proved estimates of active layer and permafrost properties can be obtained. The quality of these estimates, of course, depends on the accuracy of prior constraints used. In many instances, it may be possible to auger into this shallow layer to provide direct observations that can be used as constraints. This approach could be readily applied to the ensemble of McMC models. For example, if the resistivity of the chan-nels in Fig. 10a were known, the thickness of the chanchan-nels could be estimated more accurately by selecting only the set of McMC models with channel resistivity close to the true value, thereby removing some of the ambiguity due to equiv-alences between layer resistivity and thickness.

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much longer time periods than is practical for repeat AEM surveys. One exception could be related to infrastructure projects such as water reservoirs or mine tailing impound-ments behind dams, where AEM could be useful for baseline characterization and repeat monitoring of the impact caused by human-induced permafrost change. Geophysical model-ing, thermophysical hydrologic modelmodel-ing, and field observa-tions create a synergy that provides greater insight than any individual approach and can be useful for future characteri-zation of coupled permafrost and hydrologic processes.

5 Summary

Analysis of AEM surveys provide a means for remotely de-tecting subsurface electrical resistivity associated with the co-evolution of permafrost and hydrologic systems over ar-eas relevant to catchment-scale and larger processes. Cou-pled hydrogeophysical simulations using a novel physical property relationship that accounts for the effects of lithol-ogy, ice saturation, and temperature on electrical resistiv-ity provide a systematic framework for exploring the geo-physical response to various scenarios of permafrost evolu-tion under different hydrological forcing. This modeling ap-proach provides a means of robustly testing the interpreta-tion of AEM data given the paucity of deep boreholes and other ground truth data that are needed to characterize sub-surface permafrost. A robust uncertainty analysis of the geo-physical simulations provides important new quantitative in-formation about the types of features that can be resolved using AEM data given the inherent resolution limitations of geophysical measurements and ambiguities in the physical property relationships. In the scenarios considered here, we have shown that large-scale geologic and permafrost struc-ture is accurately estimated. Sublacustrine thaw can also be identified, but the specific geometry of partial ice saturation beneath lakes can be poorly resolved by AEM data. Under-standing the geophysical response to known simulations is helpful both for guiding the interpretation of existing AEM data and to plan future surveys and other ground-based data acquisition efforts.

Author contributions. B. J. Minsley carried out the geophysical

for-ward and inverse simulations and prepared the manuscript with con-tributions from all coauthors. T. P. Wellman and M. A. Walvoord provided SUTRA simulation results and hydrologic modeling ex-pertise. A. Revil helped to establish the petrophysical relationships used to define the electrical resistivity model used in this study.

Acknowledgements. This work was supported by the Strategic

En-vironmental Research and Development Program (SERDP) through grant no. RC-2111. We gratefully acknowledge additional support from the USGS National Research Program and the USGS Geo-physical Methods Development Project. USGS reviews provided by Josh Koch and Marty Briggs have greatly improved this manuscript.

Edited by: C. Haas

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climate, lake size, and supra- and sub-permafrost groundwater flow on lake-talik evolution, Yukon Flats, Alaska (USA), Hydro-geol. J., 21, 281–298, doi:10.1007/s10040-012-0941-4, 2013. Williams, J. R.: Geologic reconnaissance of the Yukon Flats District

Alaska, in: US Geological Survey Bulletin 1111-H, US Govern-ment Printing Office, Washington DC, 1962.

Figure

Table 1. Description of geologic units and physical properties usedin numerical simulations
Figure 2. Bulk resistivity as a function of ice saturation using thephysical properties defined for each of the lithologic units describedin Table 1.
Figure 3. SUTRA model outputs and geophysical transformations from the 6 m gaining lake simulation at 240 years
Figure 5. Mean resistivity model extracted from McMC ensembles. Results are shown for the 6 m deep hydrostatic lake scenario outputs at(a) 100 years, (b) 240 years, and (c) 1000 years.
+4

References

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